AP EAMCET201825 Apr 2018Morning ShiftMathematicsComplex NumberActual
Let A 3 - i , B 2 + i be two points in the Argand plane. If the point P represents the complex number z = x + i y , which satisfies z - 3 + i = z - 2 - i , then the locus of the point P is
Options
- Athe circle with A B as diameter
- Bthe line passing through A and B
- Cthe perpendicular bisector of A B
- Dthe ellipse with A B as major axis
Correct answer
C. the perpendicular bisector of A B
Step-by-step solution
Given, A 3 - i ⇒ A ≡ 3 , - 1 B 2 + i ⇒ B ≡ 2 , 1 Now, z - 3 + i = z - 2 - i ⇒ z - 3 - i = z - 2 + i ≡ z - A = z - B ⇒ z - 3 - i = z - 2 + i ≡ P - A = P - B Therefore, we get A P = B P . Point P is moving along the line C M such that A P = B P . Hence, locus of the point P is the perpendicular bisector of line A B .